Look at it this way. A configuration is valid if no two rooks share the same column or row. So given that there are n rows and n columns, and a rook uses up one row and one column, it doesn't really matter which row and which columns it uses, since you will have left n-1 rows and n-1 columns. Notice that once you are actually solving the problem, the position actully matters while counting because you might count choosing [(3,1) then (2,4)] and [(2,4) then (1,3)] as diferent configurations, but that's the fun part of the problem.